Assessing the effects of time-dependent restrictions and control actions to flatten the curve of COVID-19 in Kazakhstan

This article presents the assessment of time-dependent national-level restrictions and control actions and their effects in fighting the COVID-19 pandemic. By analysing the transmission dynamics during the first wave of COVID-19 in the country, the effectiveness of the various levels of control actions taken to flatten the curve can be better quantified and understood. This in turn can help the relevant authorities to better plan for and control the subsequent waves of the pandemic. To achieve this, a deterministic population model for the pandemic is firstly developed to take into consideration the time-dependent characteristics of the model parameters, especially on the ever-evolving value of the reproduction number, which is one of the critical measures used to describe the transmission dynamics of this pandemic. The reproduction number alongside other key parameters of the model can then be estimated by fitting the model to real-world data using numerical optimisation techniques or by inducing ad-hoc control actions as recorded in the news platforms. In this article, the model is verified using a case study based on the data from the first wave of COVID-19 in the Republic of Kazakhstan. The model is fitted to provide estimates for two settings in simulations; time-invariant and time-varying (with bounded constraints) parameters. Finally, some forecasts are made using four scenarios with time-dependent control measures so as to determine which would reflect on the actual situations better.

Download Full-text

TRANSMISSION DYNAMICS AND CONTROL STRATEGIES OF COVID-19 IN WUHAN, CHINA

Journal of Biological System ◽

10.1142/s0218339020500096 ◽

2020 ◽

Vol 28 (03) ◽

pp. 543-560 ◽

Cited By ~ 8

Author(s):

LIUYONG PANG ◽

SANHONG LIU ◽

XINAN ZHANG ◽

TIANHAI TIAN ◽

ZHONG ZHAO

Keyword(s):

Reproduction Number ◽

Control Strategies ◽

Public Awareness ◽

Control Measures ◽

Transmission Dynamics ◽

Published Data ◽

Model Parameters ◽

Strict Control ◽

Dynamics And Control ◽

Numerical Calculation Method

In December 2019, a novel coronavirus, SARS-COV-2, was identified among patients in Wuhan, China. Two strict control measures, i.e., putting Wuhan on lockdown and taking strict quarantine rule, were carried out to contain the spread of COVID-19. Based on the different control measures, we divided the transmission process of COVID-19 into three stages. An SEIHR model was established to describe the transmission dynamics and was applied to fit the published data on the confirmed cases of Wuhan city from December 31, 2019 to March 25, 2020 to deduce the time when the first patient with COVID-19 appeared. The basic reproduction number was estimated in the first stage to demonstrate the number of secondary infectious cases generated by an average infectious case in the absence of policy intervention. The effective reproduction numbers in second and third stages were estimated to evaluate the effects of the two strict control measures. In addition, sensitivity analysis of the reproduction number according to model parameters was executed to demonstrate the effect of the control measures for containing the spread of COVID-19. Finally, the numerical calculation method was applied to investigate the influence of the different control measures on the spread of COVID-19. The results indicated that following the strict quarantine rule was very effective, and reducing the effective contact rates and improving the diagnosis rate were crucial in reducing the effective reproduction number, and taking control measures as soon as possible can effectively contain a larger outbreak of COVID-19. But a bigger challenge for us to contain the spread of COVID-19 was the transmission from the asymptomatic carriers, which required to raising the public awareness of self-protection and keeping a good physical protection.

Download Full-text

Dynamics of swine influenza model with optimal control

Advances in Difference Equations ◽

10.1186/s13662-019-2434-4 ◽

2019 ◽

Vol 2019 (1) ◽

Author(s):

Takasar Hussain ◽

Muhammad Ozair ◽

Kazeem Oare Okosun ◽

Muhammad Ishfaq ◽

Aziz Ullah Awan ◽

...

Keyword(s):

Deterministic Model ◽

Reproduction Number ◽

Control Strategies ◽

Influenza Pandemic ◽

Swine Influenza ◽

Transmission Dynamics ◽

Model Parameters ◽

And Control ◽

Disease Free ◽

Good Agreement

AbstractTransmission dynamics of swine influenza pandemic is analysed through a deterministic model. Qualitative analysis of the model includes global asymptotic stability of disease-free and endemic equilibria under a certain condition based on the reproduction number. Sensitivity analysis to ponder the effect of model parameters on the reproduction number is performed and control strategies are designed. It is also verified that the obtained numerical results are in good agreement with the analytical ones.

Download Full-text

Analysis and prediction of the coronavirus disease epidemic in China based on an individual-based model

Scientific Reports ◽

10.1038/s41598-020-76969-4 ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Zuiyuan Guo ◽

Dan Xiao

Keyword(s):

Reproduction Number ◽

Control Measures ◽

Cumulative Number ◽

Individual Based Model ◽

Whole Process ◽

Coordinate Descent Algorithm ◽

Initial Stage ◽

The Government ◽

Prevention And Control Measures ◽

And Control

AbstractWe established a stochastic individual-based model and simulated the whole process of occurrence, development, and control of the coronavirus disease epidemic and the infectors and patients leaving Hubei Province before the traffic was closed in China. Additionally, the basic reproduction number (R0) and number of infectors and patients who left Hubei were estimated using the coordinate descent algorithm. The median R0 at the initial stage of the epidemic was 4.97 (95% confidence interval [CI] 4.82–5.17). Before the traffic lockdown was implemented in Hubei, 2000 (95% CI 1982–2030) infectors and patients had left Hubei and traveled throughout the country. The model estimated that if the government had taken prevention and control measures 1 day later, the cumulative number of laboratory-confirmed patients in the whole country would have increased by 32.1%. If the lockdown of Hubei was imposed 1 day in advance, the cumulative number of laboratory-confirmed patients in other provinces would have decreased by 7.7%. The stochastic model could fit the officially issued data well and simulate the evolution process of the epidemic. The intervention measurements nationwide have effectively curbed the human-to-human transmission of severe acute respiratory syndrome coronavirus 2.

Download Full-text

Heterogeneity and effectiveness analysis of COVID-19 prevention and control in major cities in China through time-varying reproduction number estimation

Scientific Reports ◽

10.1038/s41598-020-79063-x ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Qing Cheng ◽

Zeyi Liu ◽

Guangquan Cheng ◽

Jincai Huang

Keyword(s):

Prevention And Control ◽

Large Scale ◽

Reproduction Number ◽

Correlation Method ◽

Control Measures ◽

Time Varying ◽

Short Period ◽

Significant Difference ◽

Prevention And Control Measures ◽

And Control

AbstractBeginning on December 31, 2019, the large-scale novel coronavirus disease 2019 (COVID-19) emerged in China. Tracking and analysing the heterogeneity and effectiveness of cities’ prevention and control of the COVID-19 epidemic is essential to design and adjust epidemic prevention and control measures. The number of newly confirmed cases in 25 of China’s most-affected cities for the COVID-19 epidemic from January 11 to February 10 was collected. The heterogeneity and effectiveness of these 25 cities’ prevention and control measures for COVID-19 were analysed by using an estimated time-varying reproduction number method and a serial correlation method. The results showed that the effective reproduction number (R) in 25 cities showed a downward trend overall, but there was a significant difference in the R change trends among cities, indicating that there was heterogeneity in the spread and control of COVID-19 in cities. Moreover, the COVID-19 control in 21 of 25 cities was effective, and the risk of infection decreased because their R had dropped below 1 by February 10, 2020. In contrast, the cities of Wuhan, Tianmen, Ezhou and Enshi still had difficulty effectively controlling the COVID-19 epidemic in a short period of time because their R was greater than 1.

Download Full-text

Development of the reproduction number from coronavirus SARS-CoV-2 case data in Germany and implications for political measures

BMC Medicine ◽

10.1186/s12916-020-01884-4 ◽

2021 ◽

Vol 19 (1) ◽

Author(s):

Sahamoddin Khailaie ◽

Tanmay Mitra ◽

Arnab Bandyopadhyay ◽

Marta Schips ◽

Pietro Mascheroni ◽

...

Keyword(s):

Structural Changes ◽

Reproduction Number ◽

National Level ◽

Transmission Dynamics ◽

Federal State ◽

Parameter Estimates ◽

Time Varying ◽

Short Term ◽

Robert Koch Institute ◽

Federal States

Abstract Background SARS-CoV-2 has induced a worldwide pandemic and subsequent non-pharmaceutical interventions (NPIs) to control the spread of the virus. As in many countries, the SARS-CoV-2 pandemic in Germany has led to a consecutive roll-out of different NPIs. As these NPIs have (largely unknown) adverse effects, targeting them precisely and monitoring their effectiveness are essential. We developed a compartmental infection dynamics model with specific features of SARS-CoV-2 that allows daily estimation of a time-varying reproduction number and published this information openly since the beginning of April 2020. Here, we present the transmission dynamics in Germany over time to understand the effect of NPIs and allow adaptive forecasts of the epidemic progression. Methods We used a data-driven estimation of the evolution of the reproduction number for viral spreading in Germany as well as in all its federal states using our model. Using parameter estimates from literature and, alternatively, with parameters derived from a fit to the initial phase of COVID-19 spread in different regions of Italy, the model was optimized to fit data from the Robert Koch Institute. Results The time-varying reproduction number (Rt) in Germany decreased to <1 in early April 2020, 2–3 weeks after the implementation of NPIs. Partial release of NPIs both nationally and on federal state level correlated with moderate increases in Rt until August 2020. Implications of state-specific Rt on other states and on national level are characterized. Retrospective evaluation of the model shows excellent agreement with the data and usage of inpatient facilities well within the healthcare limit. While short-term predictions may work for a few weeks, long-term projections are complicated by unpredictable structural changes. Conclusions The estimated fraction of immunized population by August 2020 warns of a renewed outbreak upon release of measures. A low detection rate prolongs the delay reaching a low case incidence number upon release, showing the importance of an effective testing-quarantine strategy. We show that real-time monitoring of transmission dynamics is important to evaluate the extent of the outbreak, short-term projections for the burden on the healthcare system, and their response to policy changes.

Download Full-text

Estimates of the ongoing need for social distancing and control measures post-“lockdown” from trajectories of COVID-19 cases and mortality

European Respiratory Journal ◽

10.1183/13993003.01483-2020 ◽

2020 ◽

Vol 56 (1) ◽

pp. 2001483 ◽

Cited By ~ 6

Author(s):

Mike Lonergan ◽

James D. Chalmers

Keyword(s):

Severe Acute Respiratory Syndrome ◽

Economic Activity ◽

Regression Models ◽

Reproduction Number ◽

Viral Transmission ◽

Control Measures ◽

Social Distancing ◽

And Control ◽

Doubling Times

By 21 May 2020, severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) had caused more than 5 million cases of coronavirus 2019 (COVID-19) across more than 200 countries. Most countries with significant outbreaks have introduced social distancing or “lockdown” measures to reduce viral transmission. So the key question now is when, how and to what extent these measures can be lifted.Publicly available data on daily numbers of newly confirmed cases and mortality were used to fit regression models estimating trajectories, doubling times and the reproduction number (R0) of the disease, before and under the control measures. These data ran up to 21 May 2020, and were sufficient for analysis in 89 countries.The estimates of R0 before lockdown based on these data were broadly consistent with those previously published: between 2.0 and 3.7 in the countries with the largest number of cases available for analysis (USA, Italy, Spain, France and UK). There was little evidence to suggest that the restrictions had reduced R far below 1 in many places, with France having the most rapid reductions: R0 0.76 (95% CI 0.72–0.82) based on cases, and 0.77 (95% CI 0.73–0.80) based on mortality.Intermittent lockdown has been proposed as a means of controlling the outbreak while allowing periods of increased freedom and economic activity. These data suggest that few countries could have even 1 week per month unrestricted without seeing resurgence of the epidemic. Similarly, restoring 20% of the activity that has been prevented by the lockdowns looks difficult to reconcile with preventing the resurgence of the disease in most countries.

Download Full-text

Investigating the Role of Environmental Transmission in COVID-19 Dynamics: A Mathematical Model Based Study

10.21203/rs.3.rs-32476/v1 ◽

2020 ◽

Author(s):

Ibrahim M. ELmojtaba ◽

Fatma Al-Musalhi ◽

Asma Al-Ghassani ◽

Nasser Al-Salti

Keyword(s):

Mathematical Model ◽

Disease Transmission ◽

Reproduction Number ◽

Equilibrium Points ◽

Transmission Dynamics ◽

Model Parameters ◽

Environmental Transmission ◽

Estimated Parameters ◽

Existence And Stability

Abstract A mathematical model with environmental transmission has been proposed and analyzed to investigate its role in the transmission dynamics of the ongoing COVID-19 outbreak. Two expressions for the basic reproduction number R0 have been analytically derived using the next generation matrix method. The two expressions composed of a combination of two terms related to human to human and environment to human transmissions. The value of R0 has been calculated using estimated parameters corresponding to two datasets. Sensitivity analysis of the reproduction number to the corresponding model parameters has been carried out. Existence and stability analysis of disease free and endemic equilibrium points have been presented in relation with the obtained expressions of R0. Numerical simulations to demonstrate the effect of some model parameters related to environmental transmission on the disease transmission dynamics have been carried out and the results have been demonstrated graphically.

Download Full-text

COVID-19 Pandemic in India: A Mathematical Model Study

10.20944/preprints202005.0508.v1 ◽

2020 ◽

Author(s):

Sudhanshu Kumar Biswas ◽

Jayanta Kumar Ghosh ◽

Susmita Sarkar ◽

Uttam Ghosh

Keyword(s):

Population Density ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Virus Disease ◽

Control Measures ◽

High Population ◽

Model Parameters ◽

High Population Density ◽

Corona Virus ◽

Very High

The present novel corona virus (2019-nCoV) infection has created a global emergency situation by spreading all over the world in a large scale within very short time period. The infection induced death rate is also very high. There is no vaccine or anti-viral medicine for such infection. So at this moment a major worldwide problem is that how we can control this pandemic. On the other hand, India is a high population density country, where the corona virus disease (COVID-19) has started to spread from $1^{st}$ week of March, 2020 in a significant number of COVID-19 positive cases. Due to this high population density human to human social contact rate is very high in India. So control of the pandemic COVID-19 in early stage is very urgent and challenging problem. Mathematical models are employed in this paper to study the COVID-19 dynamics, to identify the influential parameters and to find the proper prevention strategies to reduce the outbreak size. In this work, we have formulated a deterministic compartmental model to study the spreading of COVID-19 and estimated the model parameters by fitting the model with reported data of ongoing pandemic in India. Sensitivity analysis has been done to identify the key model parameters. The basic reproduction number has been estimated from actual data and the effective basic reproduction number has been studied on the basis of reported cases. Some effective preventive measures and their impacts on the disease dynamics have also been studied. Future trends of the disease transmission has been Predicted from our model with some control measures. Finally, the positive measures to control the disease have been summarized.

Download Full-text

Mathematical modelling of COVID-19 transmission and control strategies in the population of Bauchi State, Nigeria

Annals of African Medical Research ◽

10.4081/aamr.2020.120 ◽

2020 ◽

Vol 3 (1) ◽

Author(s):

Yusuf Abdu Misau ◽

Nanshin Nansak ◽

Aliyu Maigoro ◽

Sani Malami ◽

Dominic Mogere ◽

...

Keyword(s):

Reproduction Number ◽

Control Strategies ◽

Research Work ◽

Control Measures ◽

High Rate ◽

World Health ◽

Contact Tracing ◽

Model Parameters ◽

Deterministic System ◽

The Novel

The novel SARS-COV-2 has since been declared a pandemic by the World Health Organization (WHO). The virus has spread from Wuhan city in China in December 2019 to no fewer than 200 countries as at June 2020 and still counting. Nigeria is currently experiencing a rapid spread of the virus amidst weak health system and more than 80% of population leaving on less than 1USD per day. To help understand the behavior of the virus in resource limited settings, we modelled the outbreak of COVID-19 and effects of control strategies in Bauchi state at north-eastern Nigeria. Using the real data of Bauchi state COVID-19 project, this research work extends the epidemic SEIR model by introducing new parameters based on the transmission dynamics of the novel COVID-19 pandemic and preventive measures. The total population of Bauchi State at the time of the study, given by is compartmentalized into five (5) different compartments as follows: Susceptible (S), Exposed (E), Infectious (I), Quarantined (Q) and Recovered (R). The new model is SEIQR. N = S → E → I → Q → R Data was collected by accessing Bauchi state electronic database of COVID-19 project to derive all the model parameters, while analysis and model building was done using Maple software. At the time of this study, it was found that the reproduction number R, for COVID-19 in Bauchi state, is 2.6 × 10-5. The reproduction number R decreased due to the application of control measures. The compartmental SEIRQ model in this study, which is a deterministic system of linear differential equations, has a continuum of disease-free equilibria, which is rigorously shown to be locallyasymptotically stable as the epidemiological threshold, known as the control reproduction number R= 0.0000026 is less than unity. The implication of this study is that the COVID-19 pandemic can be effectively controlled in Bauchi, since is R<1. Contact tracing and isolation must be increased as the models shows, the rise in infected class is a sign of high vulnerability of the population. Unless control measures are stepped up, despite high rate of recovery as shown by this study, infection rate will keep increasing as currently there is a no vaccine for COVID-19.

Download Full-text

China’s effective control and other countries’ uncharted challenge against COVID-19: an epidemiological and modelling study

10.1101/2020.04.28.20083899 ◽

2020 ◽

Author(s):

Lingling Zheng ◽

Qin Kang ◽

Weiyao Liao ◽

Xiujuan Chen ◽

Shuai Huang ◽

...

Keyword(s):

Disease Transmission ◽

Reproduction Number ◽

Case Reports ◽

Epidemiological Data ◽

Control Measures ◽

Time Dependent ◽

Effective Control ◽

List Type ◽

Global Epidemic ◽

Serial Interval

AbstractBackgroundOn the present trajectory, COVID is inevitably becoming a global epidemic, leading to concerns regarding the pandemic potential in China and other countries.ObjectiveIn this study, we use the time-dependent reproduction number (Rt) to comprise the COVID transmissibility across different countries.MethodsWe used data from Jan 20, 2019, to Feb 29, 2020, on the number of newly confirmed cases, obtained from the reports published by the CDC, to infer the incidence of infectious over time. A two-step procedure was used to estimate the Rt. The first step used data on known index-secondary cases pairs, from publicly available case reports, to estimate the serial interval distribution. The second step estimated the Rt jointly from the incidence data and the information data in the first step. Rt was then used to simulate the epidemics across all major cities in China and typical countries worldwide.ResultsBased on a total of 126 index-secondary cases pairs from 4 international regions, we estimated that the serial interval for SARS-2-CoV was 4.18 (IQR 1.92 – 6.65) days. Domestically, Rt of China, Hubei province, Wuhan had fallen below 1.0 on 9 Feb, 10 Feb and 13 Feb (Rt were 0.99±0.02, 0.99±0.02 and 0.96±0.02), respectively. Internationally, as of 26 Feb, statistically significant periods of COVID spread (Rt >1) were identified for most regions, except for Singapore (Rt was 0.92±0.17).ConclusionsThe epidemic in China has been well controlled, but the worldwide pandemic has not been well controlled. Worldwide preparedness and vulnerability against COVID-19 should be regarded with more care.What is already known on this subject?The basic reproduction number (R0) and the-time-dependent reproduction number (Rt) are two important indicators of infectious disease transmission. In addition, Rt as a derivative of R0 could be used to assess the epidemiological development of the disease and effectiveness of control measures. Most current researches used data from earlier periods in Wuhan and refer to the epidemiological features of SARS, which are possibly biased. Meanwhile, there are fewer studies discussed the Rt of COVID-19. Current clinical and epidemiological data are insufficient to help us understand the full view of the potential transmission of this disease.What this study adds?We use up-to-data observation of the serial interval and cases arising from local transmission to calculate the Rt in different outbreak level area and every province in China as well as five-top sever outbreak countries and other overseas. By comparing the Rt, we discussed the situation of outbreak around the world.

Download Full-text